Pairing symmetry which characterizes the superconducting pairing mechanism is normally determined by measuring the superconducting gap structure ($|Delta_k|$). Here, we report the measurement of a strain-induced gap modulation ($partial|Delta_k|$) in uniaxially strained Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ utilizing angle-resolved photoemission spectroscopy and $in$-$situ$ strain-tuning. We found that the uniaxial strain drives Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ into a nematic superconducting state which breaks the four-fold rotational symmetry of the superconducting pairing. The superconducting gap increases on the $d_{yz}$ electron and hole pockets while it decreases on the $d_{xz}$ counterparts. Such orbital selectivity indicates that orbital-selective pairing exists intrinsically in non-nematic iron-based superconductors. The $d_{xz}$ and $d_{yz}$ pairing channels are balanced originally in the pristine superconducting state, but become imbalanced under uniaxial strain. Our results highlight the important role of intra-orbital scattering in mediating the superconducting pairing in iron-based superconductors. It also highlights the measurement of $partial|Delta_k|$ as an effective way to characterize the superconducting pairing from a perturbation perspective.
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